Double-beta decay was considered for the first time by
Goeppert-Mayer in 1935 [1]}. The neutrino
accompanied mode of the decay with emission of electrons
(two-neutrino double-beta decay, \(2\nu 2\beta ^-\) ) is allowed in the
Standard Model of particles and interactions (SM) and is already
observed in eleven nuclei with measured half-lives in the range
\(T_{1/2}\sim (10^{19}-10^{24})\)  yr [2]}. Another
possibility could be \(2\beta ^-\)  decay without neutrino emission,
neutrinoless double-beta decay (\(0\nu 2\beta ^-\) ). However, this
process violates the lepton number conservation and is only
possible if neutrinos are massive Majorana particles
[3]}. Thus, the \(0\nu 2\beta ^-\)  decay is the most
sensitive test of the lepton number conservation law and one of
the most promising tools to study properties of the neutrino and
the weak interaction. In general, the neutrinoless process can be
mediated by many effects beyond the SM and is considered as one of
the most powerful probes of the SM
[4]}, [5]}, [6]}, [7]}.
Despite the attempts, the \(0\nu 2\beta ^-\)  decay is still not
observed: the most sensitive experiments give upper half-life
limits in the range \(\lim T_{1/2}\sim (10^{24}-10^{26})\)  yr. This
allows to bound the effective Majorana neutrino mass at the level
of \(\lim \langle m_{\nu }\rangle \sim (0.1-0.5)\)  eV (see, e.g., the
reviews
[6]}, [7]}, [10]}, [11]} and
the recent original works [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}).
